The Goodwin Manuscript
This Nero Wolfe story is a pastiche of the Old English poem Beowulf. Also, the whole story scans iambically, and if the iambs are grouped into four-foot lines they obey the alliteration rules for Old English verse: the stressed beat of the third foot alliterates with that of the first or second or both. Moreover, the alliterating words, in this case, match in initial letter as well as initial sound.
Taking the alliterating letter in each line gives ten Old English ordinals, spelled using TH instead of the Old English letter thorn (þ) or edh (ð):
EAHTA HUND AND THREO AND THRITIGOTHA (833rd)
EAHTA HUND AND SEOFOTHA (807th)
TWA THUSEND AND NIGON HUND AND TWA AND THRITIGOTHA (2932nd)
TWA AND HUNDTWELFTIGOTHA (122nd)
HUND AND SIXTIGOTHA (160th)
Taking those lines in Beowulf, and finding their alliterating letters, gives the modern English phrase (with thorn instead of th):
The twelfth word of Beowulf is the answer, ELLEN (hence the reference in the flavortext to a damsel).